portfolioAnalytics.vasicek subpackage

Functions

The Vasicek subpackage implements currently the following:

  • vasicek_base implements a finite homogeneous pool

  • vasicek_base_el implements the expected loss for the vasicek_base case

  • vasicek_base_ul implements the standard deviation for the vasicek_base case

  • vasicek_lim implements the limiting case for large N

  • vasicek_lim_el implements the expected loss for the vasicek_lim case

  • vasicek_lim_ul implements the standard deviation for the vasicek_lim case

  • vasicek_lim_q implements the quantile for the vasicek_lim case

Vasicek Base Distribution

Vasicek Base Discrete distribution.

param N

The number of entities in the portfolio

param k

The number of defaults

param p

The probability of default (uniform across the portfolio)

param rho

The asset correlation parameter

return

The probability of k defaults

Vasicek Base Distribution Expected Loss

Expected Loss for the Vasicek Base distribution.

param N

The number of entities in the portfolio

param p

The probability of default

param rho

The asset correlation (not needed here)

return

The average default rate / loss

Vasicek Base Distribution Unexpected Loss

Unexpected Loss (Standard Deviation) for the Vasicek Base distribution.

param N

The number of entities in the portfolio

param p

The probability of default

param rho

The asset correlation (not needed here)

return

The default rate volatility (UL)

Vasicek Limit Distribution

The Large-N limit of the Vasicek Distribution.

param theta

The target default rate

param p

The probability of default

param rho

The asset correlation

return

Cumulative probability

Vasicek Limit Distribution Expected Loss

The expected loss of the large n limit of the Vasicek distribution.

param p

The probability of default

param rho

The asset correlation (not needed)

return

The expected default rate

Vasicek Limit Distribution Unexpected Loss

The unexpected loss of the large n limit of the Vasicek distribution.

param p

The probability of default

param rho

The asset correlation

return

The default rate volatility

Vasicek Limit Distribution Quantile Loss

The quantile of the large-n Limit of the Vasicek distribution.

param alpha

The desired quantile

param p

The probability of default

param rho

The asset correlation

return

The default rate at that confidence level